Essential Spectrum and Mixed Type Finite Element Method

  • Takashi Kako
  • Haniffa M. Nasir
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 19)

Abstract

In the error analysis of finite element method, the inf-sup condition or the uniform lifting property plays an important role. In this paper, we discuss the relationship between the uniform inf-sup condition and the essential spectrum of the operator that appears in the problem. In general, one can not expect the convergence of the finite element approximation due to the spectral pollution that stems from the inappropriate mixing of the eigen-subspaces that correspond to two distinct components of the essential spectrum. As examples of our consideration, we treat the Stokes problem, mixed approximations of elliptic problems and a structural-acoustic coupling problem. In these problems, two distinct components might appear in the essential spectrum of the corresponding operators.

Keywords

Finite Element Method Essential Spectrum Selfadjoint Operator Stokes Problem Finite Element Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Takashi Kako
    • 1
  • Haniffa M. Nasir
    • 1
  1. 1.The University of Electro-CommunicationsChofu, TokyoJapan

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